Mitigating Supply Risk with Limited Information: Emergency Supply and Responsive Pricing

Abstract

We investigate the implications and interplay of emergency supply and responsive pricing---two effective strategies to mitigate supply risk---in response to yield randomness with limited distributional information. Specifically, we adopt a distribution-free approach to study an ambiguity-averse monopoly's joint price and production decisions given the random yield's mean and variance---arguably two of the most widely used and easy-to-estimate summary statistics. We derive for four models, which result from all possible combinations of the two strategies, closed-form solutions of the optimal price and production decisions as well as the optimal profit. Through comparative analysis, we obtain several managerial insights based on the problem's parameters, including cost parameters, demand parameters, and supply variation. The firm can benefit more from pure emergency supply than from pure responsive pricing if the unit emergency purchasing cost is not larger than a certain threshold, and the strategic relation between emergency supply and responsive pricing also critically depends on the unit emergency purchasing cost as well as the
type of distributional information we know about the random yield. We discuss how distributional information about mean and variance bridges the most and least variable situations of the random yield, thus establishing the gain and the limit of knowing variance.

Keywords: supply risk, emergency supply, responsive pricing, ambiguity aversion, distribution-free analytics.